A quantum theory of refractive index, Čerenkov radiation and the energy loss of a fast charged particle

Abstract

A quantum theory of the three related subjects of refractive index, Čerenkov radiation, and the excitation and ionization of atoms in a polarisable medium is developed. The classical theory of the electromagnetic field in a medium of extended dipoles is first written in hamiltonian form. This makes obvious a canonical transformation related to refractive index which enables one to express the total field in the medium as a superposition of oscillators. A similar transformation is made on the quantised radiation field variables, which takes account of the modified time dependence of the field due to its interaction with the medium. The processes of Čerenkov radiation and the ionization and excitation of atoms in a polarisable medium are then treated. The partition of the total energy loss between these different primary processes is obtained directly. This is done by making a perturbation expansion on the basis of physical-photon states for processes caused by the passage of a fast charged particle through the medium. For the case in which the reaction of the medium on the particle is neglected we obtain formulae which agree with those obtained previously by other authors i.e., in the first approximation the quantum theory frequently gives the same result as the classical theory for these processes.